The Hungry Streamer Theorem

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Original poster: "Steve Conner" <steve.conner-at-optosci-dot-com> 

Hi all

For my DRSSTC modelling work I needed a simple relation that would tell me
the streamer resistance and capacitance if I knew the power input.

I started by modelling the capacitance of the streamer assuming it was a
thin cone or cylinder of conductive material of roughly the same dimensions
as a streamer seemed to have. Assuming a cylinder, I got 25pF per meter of
length. (With a cone it would not be linearly proportional as the area of a
cone varies as length squared)

Next I invoked the "Hungry Streamer" theorem that says a streamer will
always grow up to the point of maximum power transfer, but no further. (I
think this was proposed on here a few years back?) If we assume the streamer
resistance is in series with its capacitance, then maximum power transfer
will be when the resistance is equal to the capacitive reactance.

So that gives 25pF per metre, and approximately 100/L kOhms (L is length in
metres) of resistance at 60kHz (it will vary with frequency)

If we substitute that into the famous "Freau formula" L=1.7*sqrt(P):

Streamer load resistance = 170/sqrt(P) kohms at 60kHz
Load capacitance= 42.5*sqrt(P) pF

This is for a series RC circuit, you can transform these values to get an
equivalent parallel RC.

Does anyone have any thoughts on the validity of this approach?

Steve C.